Evidently not. When was the last time a mainstream news organization got heat from its own viewer base because of inaccurate reporting? I mean, it's fun to dunk on fox news because you think they're obviously spewing lies or whatever, but that doesn't really matter unless their viewership actually cares. Meanwhile outrage drives clicks, so journalists are strongly incentivized to stretch the truth.
Even assuming all leads were pursued equally, and all stories were published, entertainment is still highly partisan.
Which, presumably, is why we saw partisanship jump when the entertainment component increased in revenue importance (90s talk radio, then 2000s competitive 24/7 news).
Fox News was objectively brilliant in that they saw this coming, which is why they went ahead and devoted a huge chunk of their airtime to entertainment-weighted programming.
In any case, the eyeballs are the product. The advertisers are increasingly the true customers of media outlets. They don't even theoretically care about accuracy.
A not for profit newspaper could easily have a backer with other motivations, where they might be willing to sacrifice accuracy to push a particular agenda.
I am not sure that the problem is the news. I do not think people really care if they get accurate news.